Timeline for Question about properties of affine varieties defined by bihomogeneous polynomials
Current License: CC BY-SA 3.0
4 events
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| Aug 21, 2019 at 15:47 | comment | added | Zach Teitler | However it can be replaced. An affine variety is defined by a multihomogeneous ideal if and only if it's invariant under scaling by a certain product of tori. Then its irreducible components are each, individually, also invariant; check on general points (automatic on intersections). This is a positive answer to question (1). ... If I still feel good about this idea in a few days, and if I remember, I'll update my answer above. If you're reading this comment in the year 2099, I forgot... | |
| Aug 21, 2019 at 15:41 | comment | added | Zach Teitler | I don't know what I was thinking in part (1). The irreducible set is contained in at least one irreducible component of $V$. But I don't know why it can't intersect other irreducible components. So, just containing one point of $V_i$ doesn't imply containment in $V_i$. The answer above is bogus. Sorry. | |
| Mar 19, 2017 at 21:22 | vote | accept | Johnny T. | ||
| Mar 19, 2017 at 20:22 | history | answered | Zach Teitler | CC BY-SA 3.0 |